Work

Avila's acceleration via zeros of determinants and applications to Schrödinger cocycles

Year: 2025

Type: article

Abstract: In this paper we give a characterization of Avila's quantized acceleration of the Lyapunov exponent via the number of zeros of the Dirichlet determinants in finite volume. As applications, we prove ‐Hölder continuity of the integrated density of states for supercritical quasi‐periodic Schrödinger operators restricted to the th stratum, for any and . We establish Anderson localization for all Diophantine frequencies for the operator with even analytic potential function on the first supercritical stratum, which has positive measure if it is nonempty.

Source: Communications on Pure and Applied Mathematics

DOI: 10.1002/cpa.70018

Authors: Rui Han, Wilhelm Schlag

Institutions: Louisiana State University, Yale University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Global Dynamics of Nonlinear Dispersive Evolution Equations and Spectral Theory, Dynamics of Nonlinear and Disordered Systems, CAREER: Schrödinger Operators on Lattices